Turbine distributor sector for an aircraft turbine engine, including an external annular platform sector and an internal annular platform sector, the sectors being coaxial and being connected together by blade assemblies including inner cavities cooled by gas circulation, the external platform sector including through openings of which radially internal ends open into the inner cavities, wherein the external platform sector includes inner ducts for supplying the cavities with gas, the ducts including air outlets opening into the openings and air inlets opening onto a portion of the external annular surface of the external platform sector.